Math Problem Statement

If KL = 8x, LM = 14x - 6, and KM = 16, what is KL?

Solution

We are given that:

  • KL=8xKL = 8x
  • LM=14x6LM = 14x - 6
  • KM=16KM = 16

Since K,L,MK, L, M lie on a straight line, the sum of KLKL and LMLM must equal KMKM:

KL+LM=KMKL + LM = KM

Substitute the given expressions for KLKL, LMLM, and KMKM:

8x+(14x6)=168x + (14x - 6) = 16

Simplify the left-hand side:

8x+14x6=168x + 14x - 6 = 16

22x6=1622x - 6 = 16

Now, solve for xx:

22x=16+622x = 16 + 6

22x=2222x = 22

x=1x = 1

Now that we have x=1x = 1, we can find KLKL:

KL=8x=8(1)=8KL = 8x = 8(1) = 8

Thus, KL=8KL = 8.

Would you like further details on this solution?

Here are some related questions for you to explore:

  1. What is the value of LMLM when x=1x = 1?
  2. What is the total length of KL+LMKL + LM?
  3. How would the result change if KM=20KM = 20 instead of 16?
  4. Can you represent this problem geometrically on a number line?
  5. What would happen if LM=10x+2LM = 10x + 2 instead?

Tip: When dealing with line segments, always remember that the sum of smaller segments must equal the total length of the larger segment.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Geometry (Line Segments)

Formulas

KL + LM = KM
Solving for x in linear equations

Theorems

Segment Addition Postulate (the sum of smaller segments equals the total segment)

Suitable Grade Level

Grades 6-8